Answer

The solution is $\Big(-\infty,-\dfrac{2}{3}\Big)\cup\Big(4,\infty\Big)$

Work Step by Step

$|5-3x|\gt7$
Solving this absolute value inequality is equivalent to solving two separate inequalities, which are:
$5-3x\gt7$ and $5-3x\lt-7$
$\textbf{Solve the first inequality:}$
$5-3x\gt7$
Take $5$ to the right side:
$-3x\gt7-5$
$-3x\gt2$
Take $3$ to divide the right side and reverse the inequality sign:
$x\lt-\dfrac{2}{3}$
$\textbf{Solve the first inequality:}$
$5-3x\lt-7$
Take $5$ to the right side:
$-3x\lt-7-5$
$-3x\lt-12$
Take $3$ to divide the right side and reverse the inequality sign:
$x\gt\dfrac{-12}{-3}$
$x\gt4$
Expressing the solution in interval notation:
$\Big(-\infty,-\dfrac{2}{3}\Big)\cup\Big(4,\infty\Big)$